Is there a Catholic God?

‘We all adore the same God’… This type of expression, of significant theological imprecision, is often to be heard when of people from different religions engage in careless ecumenical chatter.

But, to be little more precise, how can the Triune God, Who revealed Himself to humanity in the incarnation of the Word and ordered men to be baptized in His name, be the same deity preached by others, for example, by Islam?